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Three squares are based on the sides of a right angled triangle. The area of the two smaller ones are 144 sq. cm and 256 sq. cm. What is the area of the third one?​
  • a)
    625 sq. cm
  • b)
    361 sq. cm
  • c)
    400 sq. cm
  • d)
    900sq. cm
Correct answer is option 'C'. Can you explain this answer?
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Solution:

Given:
- Area of the two smaller squares = 144 sq. cm and 256 sq. cm

Let's find the sides of the squares:
- Let the sides of the squares be a, b, and c where a and b are the sides of the smaller squares, and c is the side of the larger square.
- Area of a square = Side x Side

For the smaller squares:
- Side of the first square (a) = √144 = 12 cm
- Side of the second square (b) = √256 = 16 cm

For the third square:
- The third square is based on the hypotenuse of the right-angled triangle.
- By Pythagoras theorem: c² = a² + b²
- c² = 12² + 16²
- c² = 144 + 256
- c² = 400
- Side of the third square (c) = √400 = 20 cm

Area of the third square:
- Area = Side x Side
- Area = 20 x 20
- Area = 400 sq. cm
Therefore, the area of the third square is 400 sq. cm.
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Three squares are based on the sides of a right angled triangle. The area of the two smaller ones are 144 sq. cm and 256 sq. cm. What is the area of the third one?a)625 sq. cmb)361 sq. cmc)400 sq. cmd)900sq. cmCorrect answer is option 'C'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Three squares are based on the sides of a right angled triangle. The area of the two smaller ones are 144 sq. cm and 256 sq. cm. What is the area of the third one?a)625 sq. cmb)361 sq. cmc)400 sq. cmd)900sq. cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three squares are based on the sides of a right angled triangle. The area of the two smaller ones are 144 sq. cm and 256 sq. cm. What is the area of the third one?a)625 sq. cmb)361 sq. cmc)400 sq. cmd)900sq. cmCorrect answer is option 'C'. Can you explain this answer?.
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